A process of the type mentioned in the introduction is described, for example, in US 2005/0255240 A1, in which pipes having a relatively narrow cross section are intended to be coated from the inside. This is done by immersing these pipes in a solution containing the coating material, said solution being sucked into the pipes owing to the effective capillary forces. This process can be further assisted by applying a vacuum to the free end of the pipe. As soon as the pipe is filled with the fluid, a sleeve which surrounds the pipe is used to introduce thermal energy into said pipe, this treatment being started at the free end, i.e. the end which is not immersed in the fluid. The solvent is thereby evaporated and leaves the pipe at the top, while the polymer dissolved in the solvent is deposited on the inner walls of the pipe. When the heating sleeve reaches the opposite end of the pipe, the coating process is complete and the layer is completed. As soon as the sleeve has locally heated a point on the pipe and is moved on, this point cools down to room temperature again.